Today, because it is impossible to do it in a kosher way, we must perform the ritual with money. Rabbinic sources including the Chayei Adam and Mishna Berurah are clear that when the ritual cannot be performed in a kosher way it is preferable to use money.
I once was enamored of this ancient ritual whereby the sins of a person are symbolically transferred to the chicken, which is then slaughtered and given to the poor to eat. It was exotic. But no more. I find it reprehensible for Jews to behave this way to animals.